WASHINGTON — Over the weekend, President Trump was accused by a Republican senator of running the White House like a “reality show.” In the 48 hours that followed, this is how the president rebutted the characterization.

He called out the offending senator for being short and sounding like “a fool.” He challenged his secretary of state to an I.Q. contest and insisted he would win. He celebrated the downfall of a critic who was suspended from her job. And his first wife and third wife waged a public war of words over who was really his first lady.

Mr. Trump’s West Wing has always seemed to be the crossroads between cutthroat politics and television drama, presided over by a seasoned showman who has made a career of keeping the audience engaged and coming back for more. Obsessed by ratings and always on the hunt for new story lines, Mr. Trump leaves the characters on edge, none of them ever really certain whether they might soon be voted off the island.

“Absolutely, I see those techniques playing out,” said Laurie Ouellette, a communications professor at the University of Minnesota who has studied reality television extensively. “Reality TV is known for its humiliation tactics and its aggressive showmanship and also the idea that either you’re in or you’re out, with momentum building to the final decision on who stays and who goes.”

Among those on the in-or-out bubble in this week’s episode was Senator Bob Corker of Tennessee, the frustrated Republican who described — and derided — the conversion of the White House into a virtual set for “The Apprentice” and, for good measure, expressed concern in a weekend interview with The New York Times that the president could stumble the country into a nuclear war.

Mr. Trump, who hosted “The Apprentice” on NBC for 14 seasons, dismissed Mr. Corker on Tuesday by mocking his height and suggesting he had somehow been conned. “The Failing @nytimes set Liddle’ Bob Corker up by recording his conversation,” Mr. Trump wrote. “Was made to sound a fool, and that’s what I am dealing with!”

In labeling Mr. Corker “liddle,” the president was evidently returning to a theme. He considered Mr. Corker for secretary of state during the transition after last year’s election but was reported to have told associates that Mr. Corker, at 5-foot-7, was too short to be the nation’s top diplomat. Instead, Mr. Trump picked Rex W. Tillerson, who is several inches taller but whose own relationship with the president has deteriorated to the point that he was said to have called Mr. Trump a “moron.”

Mr. Tillerson initially did not deny it, but later he had a spokeswoman insist that he did not say it. Mr. Trump chose to believe the denial, or at least said he did, but in an interview published Tuesday, he insisted that even if it was true, he could prove that he was actually smarter than his secretary of state.

“I think it’s fake news,” Mr. Trump told Forbes magazine. “But if he did that, I guess we’ll have to compare I.Q. tests. And I can tell you who is going to win.”

Mr. Trump later denied that he had demeaned his secretary of state. “I didn’t undercut anybody. I don’t believe in undercutting people,” he told reporters, in a comment that must have amused the many people he has undercut since taking office. Asked if he still had confidence in Mr. Tillerson, Mr. Trump said simply, “Yes.”

At the time, Mr. Trump was sitting next to Henry Kissinger, the former secretary of state who happened to be visiting the Oval Office on Tuesday. To be sure, Mr. Kissinger would hardly tower over Mr. Corker on the basketball court, but Mr. Trump, perhaps wisely, did not risk challenging the former diplomat to an I.Q. contest.

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Mr. Trump said on Tuesday that he still had confidence in Rex W. Tillerson, his secretary of state.CreditDoug Mills/The New York Times

After the meeting with Mr. Kissinger, the president headed to a lunch with Mr. Tillerson, who was joined by a mediator, Defense Secretary Jim Mattis. Sarah Huckabee Sanders, the White House press secretary, said they “had a great visit” and denied that Mr. Trump was serious about the I.Q. test. “He made a joke, nothing more than that,” she said.

Mr. Trump was not joking when he took a shot earlier in the day at Jemele Hill, the ESPN host who has called him a white supremacist and was suspended on Monday for suggesting a boycott of the Dallas Cowboys’ advertisers if the team punished players who protested racial injustice by kneeling during the national anthem.

“With Jemele Hill at the mike, it is no wonder ESPN ratings have ‘tanked,’ in fact, tanked so badly it is the talk of the industry!” Mr. Trump wrote on Twitter.

He made no mention of the other dust-up in his household. In an interview aired on Monday to promote her new memoir, Ivana Trump, his first wife, told ABC News that “I’m basically first Trump wife, O.K.? I’m first lady, O.K.?”

That did not sit well with Melania Trump, his third wife and the actual first lady, who issued a retort through a spokeswoman dismissing what she called “attention-seeking and self-serving noise.”

Andy Cohen, the creator of the “Real Housewives” reality television show franchise, found that too rich. “This is actually happening,” he wrote on Twitter. “All the wives are fighting. Even I AM SPEECHLESS.”

Mr. Trump’s gibe at Mr. Corker echoed his name calling during the presidential campaign when he labeled Senator Marco Rubio of Florida “Little Marco,” Senator Ted Cruz of Texas “Lyin’ Ted” and Hillary Clinton “Crooked Hillary.” He has used belittling nicknames to diminish political foes since taking office, as well — think “Cryin’ Chuck” Schumer, “Psycho Joe” Scarborough and “Little Rocket Man” Kim Jong-un — but has generally avoided doing so with powerful Republican committee chairmen who control appointments and legislation.

It was not clear what Mr. Trump meant when he said The Times set up Mr. Corker by recording him. Angry that Mr. Corker had suggested he was an agent of “chaos,” Mr. Trump lashed out at the senator on Sunday by saying he “didn’t have the guts” to run for another term. A Times reporter then interviewed Mr. Corker by telephone and recorded the call with the senator’s knowledge and consent. Mr. Corker’s staff also recorded the call, and he said he wanted The Times to do the same.

During the interview, Mr. Corker said Mr. Trump’s advisers were struggling to keep the president under control. “I know for a fact that every single day at the White House, it’s a situation of trying to contain him,” he said. He also said Mr. Trump’s reckless statements could put the country on a path “towards World War III.”

Mr. Trump on Tuesday rejected the suggestion that he was risking a nuclear war. “We were on the wrong path before,” he said, presumably referring to North Korea. “All you have to do is take a look. If you look over the last 25 years through numerous administrations, we were on a path to a very big problem, a problem like this world has never seen. We’re on the right path right now, believe me.”

But what a path. Ms. Ouellette, who has written or edited several books on reality television, including “Better Living Through Reality TV,” said Mr. Trump the president had gone even further than Mr. Trump the reality show star ever did.

“This has exceeded what would have been allowed on ‘The Apprentice,’” she said. “It’s almost a magnification. It’s like reality TV unleashed. Yes, he was good at it, but I always felt like he had to be reined in in order not to mess up the formula. Here, he doesn’t have that same sort of constraint.”

A version of this article appears in print on , Section A, Page 16 of the New York edition with the headline: Caught in Bright Lights of a Reality Show That Never Ends. Order Reprints | Today’s Paper | Subscribe